A112173 McKay-Thompson series of class 36b for the Monster group.

1, 2, 1, 4, 8, 6, 10, 16, 18, 26, 33, 40, 58, 74, 82, 112, 147, 166, 212, 268, 316, 392, 476, 560, 695, 838, 967, 1184, 1430, 1648, 1970, 2352, 2731, 3236, 3803, 4404, 5206, 6080, 6984, 8192, 9553, 10942, 12709, 14736, 16886, 19506, 22448, 25648

Offset

0,2

Comments

Convolution square of A112206. - Vaclav Kotesovec, Sep 08 2015

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

Formula

a(n) ~ exp(2*Pi*sqrt(n)/3) / (2*sqrt(3)*n^(3/4)). - Vaclav Kotesovec, Sep 08 2015

Expansion of q^(1/3)*((eta(q^2)*eta(q^6))^2/(eta(q)*eta(q^3)*eta(q^4)* eta(q^12)))^2 in powers of q. - G. C. Greubel, Jun 16 2018

Expansion of abs(q^(1/3)*(eta(q)*eta(q^3)/(eta(q^2)*eta(q^6)))^2) in powers of q. - G. C. Greubel, Jun 16 2018

Example

T36b = 1/q +2*q^2 +q^5 +4*q^8 +8*q^11 +6*q^14 +10*q^17 +...

Mathematica

nmax = 60; CoefficientList[Series[Product[((1 + x^k)*(1 + x^(3*k)) / ((1 + x^(2*k))*(1 + x^(6*k))))^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 08 2015 *)
eta[q_]:= q^(1/24)*QPochhammer[q];  a:= CoefficientList[Series[q^(1/3)*((eta[q^2]*eta[q^6])^2/(eta[q]*eta[q^3]*eta[q^4]*eta[q^12]))^2, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 16 2018 *)

Prog

(PARI) q='q+O('q^50); A = ((eta(q^2)*eta(q^6))^2/(eta(q)*eta(q^3)* eta(q^4)*eta(q^12)))^2; Vec(A) \\ G. C. Greubel, Jun 16 2018

Crossrefs

Cf. A112206.

Sequence in context: A158451 A257706 A118272 * A058543 A353661 A156817

Adjacent sequences: A112170 A112171 A112172 * A112174 A112175 A112176

Keyword

nonn

Author

Michael Somos, Aug 28 2005

Status

approved